I'm puzzled by one thing concerning Laurent series. If I have a series, for example f(z) =(z*sinz)/(2z-1) and I'm supposed to make a laurent series of f about the point z=1/2. Now, what would the inner and outer radius of convergence be? I would say that since z=1/2 is a pole, the inner radius is zero and the outer radius infinite? If not, then how can I see the radius of convergence of a Laurent series?